That adapter was a short term solution for a period of time before usb c. The right side of the adapter is a normal mini b connector and the left side is there to handle the extra power that is allowed to pass through for the usb 3 spec.
The hdd seems to be operating at normal speeds for it. The SSD should transfer about 4-5 times faster than the hdd.
Since you are testing, I assume your SSD is mostly empty. As an SSD fills, its write speed will slow down. Even then I wouldn’t expect results that poor. My old work issued MBP with 128GB would write at usb 2.0 speeds when it was about 3/4 full. Same with my M1 mini, speeds drop as it fills.
Is the usb c to usb c cable the one that came from Crucial? If not, it could be a power delivery cable not meant to carry data at high speed. I would recommend trying a usb c to usb c cable that mentions data speeds of 5 gb/s (usb 3.0) or higher. The higher spec’d ones are backward compatible. Or better yet, a single usb c to usb a cable, again, check for the data speeds.
It sounds like your adapter should be usb 3, but it’s another possible culprit. I’d go the single cable route though, if I’m buying new parts.